Very low sensitivity FIR filter implementation using 'structural passivity' concept

The concept of "structurally bounded" or "structurally passive" FIR filter implementation is introduced, as a means of achieving very low passband sensitivities. The resulting filter structures, called FIRBR structures, can easily be transformed into very low-sensitivity "passive" two-dimensional FIR filter structures. From a layout point of view, the new structures are not any more complicated than the well-known cascade form. The FIRBR structures do not depend, for synthesis, upon continuous-time filter circuits

Fast implementation of a general L/M rate changer by a filter bank structure

In this paper, we show that an L/M rate changer can be realized as a discrete time SISO (L,M) shift invariant system in form of a two-dimensional kernel function or a filter bank structure. Based on this realization, we can implement an L/M rate changer by a bank of filters with the average number of the coefficients in the filters in each channel is 1/L of the original L/M rate changer. Hence, the system is speed up by L. This helps the designer to design a sharp cutoff discrete time FIR filters in an L/M rate changer for some real time applications in video systems

A new class of two-channel biorthogonal filter banks and wavelet bases

We propose a novel framework for a new class of two-channel biorthogonal filter banks. The framework covers two useful subclasses: i) causal stable IIR filter banks. ii) linear phase FIR filter banks. There exists a very efficient structurally perfect reconstruction implementation for such a class. Filter banks of high frequency selectivity can be achieved by using the proposed framework with low complexity. The properties of such a class are discussed in detail. The design of the analysis/synthesis systems reduces to the design of a single transfer function. Very simple design methods are given both for FIR and IIR cases. Zeros of arbitrary multiplicity at aliasing frequency can be easily imposed, for the purpose of generating wavelets with regularity property. In the IIR case, two new classes of IIR maximally flat filters different from Butterworth filters are introduced. The filter coefficients are given in closed form. The wavelet bases corresponding to the biorthogonal systems are generated. the authors also provide a novel mapping of the proposed 1-D framework into 2-D. The mapping preserves the following: i) perfect reconstruction; ii) stability in the IIR case; iii) linear phase in the FIR case; iv) zeros at aliasing frequency; v) frequency characteristic of the filters

On the eigenfilter design method and its applications: a tutorial

The eigenfilter method for digital filter design involves the computation of filter coefficients as the eigenvector of an appropriate Hermitian matrix. Because of its low complexity as compared to other methods as well as its ability to incorporate various time and frequency-domain constraints easily, the eigenfilter method has been found to be very useful. In this paper, we present a review of the eigenfilter design method for a wide variety of filters, including linear-phase finite impulse response (FIR) filters, nonlinear-phase FIR filters, all-pass infinite impulse response (IIR) filters, arbitrary response IIR filters, and multidimensional filters. Also, we focus on applications of the eigenfilter method in multistage filter design, spectral/spacial beamforming, and in the design of channel-shortening equalizers for communications applications

Approximation of L\"owdin Orthogonalization to a Spectrally Efficient Orthogonal Overlapping PPM Design for UWB Impulse Radio

In this paper we consider the design of spectrally efficient time-limited pulses for ultrawideband (UWB) systems using an overlapping pulse position modulation scheme. For this we investigate an orthogonalization method, which was developed in 1950 by Per-Olov L\"owdin. Our objective is to obtain a set of N orthogonal (L\"owdin) pulses, which remain time-limited and spectrally efficient for UWB systems, from a set of N equidistant translates of a time-limited optimal spectral designed UWB pulse. We derive an approximate L\"owdin orthogonalization (ALO) by using circulant approximations for the Gram matrix to obtain a practical filter implementation. We show that the centered ALO and L\"owdin pulses converge pointwise to the same Nyquist pulse as N tends to infinity. The set of translates of the Nyquist pulse forms an orthonormal basis or the shift-invariant space generated by the initial spectral optimal pulse. The ALO transform provides a closed-form approximation of the L\"owdin transform, which can be implemented in an analog fashion without the need of analog to digital conversions. Furthermore, we investigate the interplay between the optimization and the orthogonalization procedure by using methods from the theory of shift-invariant spaces. Finally we develop a connection between our results and wavelet and frame theory.Comment: 33 pages, 11 figures. Accepted for publication 9 Sep 201